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After 100 years of effort, the classification of all the finite subgroups ofSU(3) is yet incomplete. The most recently updated list can be found in P.O.Ludl, J. Phys. A: Math. Theor. 44 255204 (2011), where the structure of theseries (C) and (D) of SU(3)-subgroups is studied. We provide a minimal set ofgenerators for one of these groups which has order 162. These generators appearup to phase as the image of an irreducible unitary braid group representationissued from the Jones-Kauffman version of SU(2) Chern-Simons theory at level 4.In light of these new generators, we study the structure of the group in detailand recover the fact that it is isomorphic to the semidirect product Z_9 \timesZ_3 \rtimes S_3 with respect to conjugation.

A new set of generators and a physical interpretation for the SU(3) finite subgroup D(9,1,1;2,1,1)